Reduce to lowest terms: $- \dfrac{5}{9} \div - \dfrac{8}{3} = {?}$
Explanation: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{8}{3}$ is $- \dfrac{3}{8}$ Therefore: $ - \dfrac{5}{9} \div - \dfrac{8}{3} = - \dfrac{5}{9} \times - \dfrac{3}{8} $ $ \phantom{- \dfrac{5}{9} \times - \dfrac{3}{8}} = \dfrac{-5 \times -3}{9 \times 8} $ $ \phantom{- \dfrac{5}{9} \times - \dfrac{3}{8}} = \dfrac{15}{72} $ The numerator and denominator have a common divisor of $3$, so we can simplify: $ \dfrac{15}{72} = \dfrac{15 \div 3}{72 \div 3} = \dfrac{5}{24} $